Q: Consider a conducting tube with inner radius $$R_1 = 1.0$$\ \mathrm{m}$$ and outer radius R_2$ = 2.0\ \mathrm{m}. $$Suppose that current $$I = 4.0\ \mathrm{A} is $$flowing out of the page, uniformly distributed across the cross-section of the tube. What is the magnitude of the magnetic field at $$r = 1.5\ \mathrm{m}$$?

$$3.0 \times 10$$^{-7}$$\ \mathrm{T}$$

Q: A circular conducting loop with a resistance of $$0.15\ \Omega$$ and a radius of $$0.20\ \mathrm{m} is in a $$uniform magnetic field that is applied into the page. In a duration of $$15\ \mathrm{s}$$, the magnetic flux through the loop decreases steadily by $$7.0 \times 10$$^{-3}$$\ \mathrm{T} \cdot \mathrm{m}^2. $$What is the time rate of change of the applied magnetic field?

$$1.9 \times 10$$^{-3}$$\ \mathrm{T/s}$$

Q: Is there current flowing in the loop? If so, what is the current?

Yes. $$3.1 \times 10$$^{-3}$$\ \mathrm{A}$$, clockwise

Question 1

For a given potential difference across a length of wire, which of the following changes would result in an increase in the amount of current flowing through the wire by a factor of 9?

Accepted Answer

Use a wire made of a material with a conductivity that is 9 times the conductivity of the original wire

Question 2

Three resistors and three batteries are connected as shown in the circuit. Which of the following equations is a correct application of Kirchhoff's loop rule applied to the left loop, starting at junction P and proceeding in the clockwise direction?

Accepted Answer

$$-I_2$ R_2$ + \$$varepsilon_2$$ + I_1$ R_1$ + \$$varepsilon_1$$ = 0$$

Question 3

If $$2.0\ \mathrm{A} of $$current flows from A to B, what is the potential difference $$V_B - V_A$$?

Accepted Answer

$$7.0\ \mathrm{V}$$

Question 4

Consider a conducting tube with inner radius $$R_1 = 1.0$$\ \mathrm{m}$$ and outer radius R_2$ = 2.0\ \mathrm{m}. $$Suppose that current $$I = 4.0\ \mathrm{A} is $$flowing out of the page, uniformly distributed across the cross-section of the tube. What is the magnitude of the magnetic field at $$r = 1.5\ \mathrm{m}$$?

Accepted Answer

$$3.0 	imes 10$$^{-7}$$\ \mathrm{T}$$

Question 5

A solenoid with a length of $$2.2\ \mathrm{m}$$ and a radius of $$0.025\ \mathrm{m}$$ has $$1.5 	imes 10^3$ turns. The current flowing in it is given by I(t) = (3.0$$\ \mathrm{A}) \sin((0.50\ \mathrm{s}^{-1})t)$$. What is the absolute value of the induced emf in the inductor at t = 5.0$$\ \mathrm{s}$$?

Accepted Answer

$$61\ \mathrm{V}$$

Question 6

At $$t = 0\ \mathrm{s}$$, is the magnetic energy stored in the inductor at its maximum, minimum, or somewhere in between?

Accepted Answer

Minimum

Question 7

Consider the two current-carrying wires shown. The current in wire 1 is $$I_0$$; the current in wire 2 is adjusted to make the net magnetic field at point A equal to zero. Find the magnitude of the current in wire 2 in terms of $$I_0.$$

Accepted Answer

$$I_0/3$

Question 8

A potential difference of $$0.050\ \mathrm{V} is $$developed across a $$0.10\ \mathrm{m}-$$long wire as it moves through a magnetic field at $$5.0\ \mathrm{m/s}. $$The magnetic field is perpendicular to the axis of the wire. What are the direction and strength of the magnetic field?

Accepted Answer

$$0.10\ \mathrm{T}$$, out of the page

Question 9

A circular conducting loop with a resistance of $$0.15\ \Omega$$ and a radius of $$0.20\ \mathrm{m} is in a $$uniform magnetic field that is applied into the page. In a duration of $$15\ \mathrm{s}$$, the magnetic flux through the loop decreases steadily by $$7.0 	imes 10$$^{-3}$$\ \mathrm{T} \cdot \mathrm{m}^2. $$What is the time rate of change of the applied magnetic field?

Accepted Answer

$$1.9 	imes 10$$^{-3}$$\ \mathrm{T/s}$$

Question 10

Is there current flowing in the loop? If so, what is the current?

Accepted Answer

Yes. $$3.1 	imes 10$$^{-3}$$\ \mathrm{A}$$, clockwise

Question 11

For the current flowing in the loop shown, which of the following expressions gives the magnitude of the magnetic field at P?

Accepted Answer

$$\frac{\mu_0$ I}{8R}$$

Question 12

A positively charged particle is moving at a constant velocity of $$v = c/2 in $$the positive x-direction. The figure shows the moment when the particle is at the origin. Positions S and T are on the x and y axes, respectively, and are the same distance away from the origin. Which of the following comparisons of the electric field, $$E$$, and magnetic field, $$B$$, measured at S and T at the moment shown, is correct?

Accepted Answer

$$E_T = E_S$$ and $$B_T \u003e B_S$$

Question 13

A circular parallel plate capacitor with radius $$R is $$charging. Assume the electric field is uniform between the plates, shown in the shaded region in the diagram at right, and zero elsewhere at any given instant. Consider two concentric circular paths, one with a radius of $$3R/2$$ and $$R/2$$, respectively. Compare the magnitude of the magnetic field along the two paths, B1 and B2.

Accepted Answer

$$B_1$$ \u003c $$B_2$$

Question 14

A solenoid with a length of $$1.5\ \mathrm{m}$$ and radius $$0.12\ \mathrm{m}$$ has $$9500$$ windings. Initially, it carries $$25\ \mathrm{A} of $$current, which establishes a magnetic field inside the solenoid. What is the energy stored in the magnetic field inside the solenoid?

Accepted Answer

$$2400\ \mathrm{J}$$

Question 15

If the current in the solenoid now steadily decreases to zero in $$30\ \mathrm{s}$$, what is the induced emf in the solenoid?

Accepted Answer

$$2.9\ \mathrm{V}$$

Question 16

A long straight wire carries current $$I$$ uniformly over its circular cross-section with a radius $$R. $$What is the magnitude of the magnetic field inside the wire at a distance $$r$$ ($$r \u003c R) $$away from the central axis of the wire?

Accepted Answer

$$\frac{\mu_0$ I r}{2 \pi R^2$}$$

Question 17

Three light bulbs A, B, and C are connected to an ideal battery as shown. Bulb A has a resistance of $$R_A$$, bulb B has a resistance of $$R_B$$, and bulb C has a resistance of $$R_C. If $$bulb A and bulb B are of the same brightness, and bulb C is dimmer than either of them, compare the resistances of the bulbs.

Accepted Answer

$$R_A = R_B \u003c R_C$$

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